Q2 REMAINDERS

A is the set of positive integers such that when divided by 2,3,4,5,6 leaves the remainders 1,2,3,4,5 respectively. How many integers between 0 and 100 belong to set A?

  a. 0

  b. 1

  c. 2

Required number of the set is calculated by the LCM of (2, 3, 4, 5, 6) - (common difference)

In this case, common difference = (2-1) = (3-2) = (4-3) = (5- 4) = (6 - 5) = 1.

All integers of the set will be given by (60n - 1) ;

If n = 1, (60 - 1) = 59;

If n = 2,((60*2) - 1) = 119;

Since range of the set A is between 0 and 100,

hence there will exist only one number i.e., 59.

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